This is most likely happening due to a hidden power option called System unattended sleep timeout. On my machine it was set to 2 minutes, which was mighty annoying, as it would cause behavior described by OP (sleep, wake-up, login screen, Event Viewer saying: "The system is entering sleep; Sleep Reason: System Idle"). You have to enable this option in registry before being able to change it.

From http://answers.microsoft.com/en-us/windows/forum/windows_10-windows_install/windows-10-keeps-going-into-sleep-after-1-minute:

1. Click on the windows icon
2. Type regedit
3. Right-click on regedit icon, click Run as administrator
4. Go to HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Power\PowerSettings\238C9FA8-0AAD-41ED-83F4-97BE242C8F20\7bc4a2f9-d8fc-4469-b07b-33eb785aaca0
5. Double click on Attributes
6. Enter number 2.
7. Go to Advanced power settings (click on Windows button, write power options, click on Power Options, in the selected plan click on the Change plan settings, click on the Change advanced power settings).
8. Click on the Change settings that are currently unavailable
9. Click Sleep, then System unattended sleep timeout, then change these settings from 2 Minutes to 20 for example.

This solved the issue for me.

If your computer participates in a domain, it is normal that the properties of the Windows Time system service are not modifiable. They would be grayed out by default and the time is synchronized with the domain controller, as required for Kerberos authentication. You should in this case address yourself to the administrator of the domain.

If your computer is not on a domain, check first if this also happens when booting in Safe mode. If the Properties are still not modifiable, then there is a problem with Windows. Otherwise, some installed product is causing the problem.

If this also happens in Safe mode, check in the Local Group Policy Editor (gpedit.msc) if the permissions have not been corrupted.

Position to Computer Configuration\Windows Settings\Security Settings\Local Policies\User Rights Assignment. Check here the item Change the system time whose property should be LOCAL SERVICE,Administrators,NT SERVICE\autotimesvc. Check also Change the time zone whose value should be LOCAL SERVICE,Administrators,Users,Device Owners.

If this is not the problem, to set all Windows components to a known state would require to Do a Repair Install of Windows 10 with an In-place Upgrade. This is exactly the same as doing a major Windows upgrade, so you should take similar precautions, but in most cases has no bad effects.